In an interference experiment, the ratio of the amplitudes of two coherent waves is \(\dfrac{a_1}{a_2}=\dfrac{1}{3}.\) The ratio of the maximum and minimum intensities of the fringes will be:

Interference fringes are observed on a screen by illuminating two thin slits \(1\) mm apart with a light source (\(\lambda =632.8~\mathrm{nm}\)). The distance between the screen and the slits is \(100\) cm. If a bright fringe is observed on a screen at a distance of \(1.27\) mm from the central bright fringe, then the path difference between the waves, which are reaching this point from the slits is close to:
1. \(1.27~\mathrm{\mu m}\)
2. \(2~\mathrm{nm}\)
3. \(2.87~\mathrm{nm}\)
4. \(2.05~\mathrm{\mu m}\)
 

Two coherent sources of sound, \(S_1\) and \(S_2\), produce sound waves of the same wavelength, \(\lambda=1~\mathrm{m}\), in phase. \(S_1\) and \(S_2\) are placed \(1.5\) m apart (see fig.) A listener, located at \(L\), directly in front of \(S_2\) finds that the intensity is at a minimum when he is \(2\) m away from \(S_2\). The listener moves away from \(S_1\), keeping his distance from \(S_2\) fixed. The adjacent maximum of intensity is observed when the listener is at a distance \(d\) from \(S_1\). Then, \(d\) is:

1. \(12~\text{m}\)
2. \(3~\text{m}\)
3. \(5~\text{m}\)
4. \(2~\text{m}\)

In the figure below, \(P\) and \(Q\) are two equally intense coherent sources emitting radiation of wavelength \(20~\text{m}.\) The separation between \(P\) and \(Q\) is \(5~\text{m}\) and the phase of \(P\) is ahead of that of \(Q\) by $\mathrm{}$\(90^\circ.\) \(A,\) \(B\) and \(C\) are three distinct points of observation each equidistant from the midpoint of \(PQ.\) The intensities of radiation at \(A,\) \(B,\) \(C\) will be ratio: 

                       
1. \(4:1:0\)
2. \(2:1:0\)
3. \(0:1:2\)
4. \(0:1:4\)

Two coherent light sources produce an interference pattern, with their intensities in the ratio of \(2x.\) What is the value of the ratio \(\dfrac{{I}_{\max }-{I}_{\min }}{{I}_{\max }+{I}_{\min }}\text{?}\)
1. \( \dfrac{2 \sqrt{2 x}}{x+1} \)
2. \(\dfrac{\sqrt{2 x}}{2 x+1} \)
3. \(\dfrac{\sqrt{2 x}}{x+1} \)
4. \(\dfrac{2 \sqrt{2 x}}{2 x+1}\)